We propose a new approach that allows one to reduce nonlinear equations on Lie groups with fewer number of independent variables for finding particular solutions the equations. The main idea is apply method noncommutative integration linear part equation, which find bases in space partial differential set noncommuting symmetry operators. implemented generalized Schrödinger equation group curved...

Does the equation x+y+z = 29 have a solution in integers? Yes: (3, 1, 1), for instance. How about x+y+z = 30? Again yes, although this was not known until 1999: the smallest solution is (−283059965,−2218888517, 2220422932). And how about x+y+z = 33? This is an unsolved problem. Of course, number theory does not end with the study of cubic equations in three variables: one might ask also about x...

In  this paper, we investigate the generalizedHyers-Ulam-Rassias stability for the quartic, cubic and additivefunctional equation$$f(x+ky)+f(x-ky)=k^2f(x+y)+k^2f(x-y)+(k^2-1)[k^2f(y)+k^2f(-y)-2f(x)]$$ ($k in mathbb{Z}-{0,pm1}$) in $p-$Banach spaces.

Thesis Work on Algebraic Geometry The homogeneous cubic polynomials in four variables x, y, z and w form a 20 dimensional vector space over C. Let S ⊂ P be a surface defined by the equation f(x, y, z, w) = a0x 3 + a1x y + · · ·+ a19w = 0, which naturally determines a point [a0, . . . , a19] ∈ P. X admits a natural G = SL(4;C) action. Let X denote the smooth cubic surfaces, X the semistable ones...

The phonon instability and thermal equation of state of Mo are extensively investigated using density functional theory. The calculated phonon dispersion curves agree well with experiments. Under compression, we captured a large softening in the transverse acoustic (TA) branches of body-centred cubic Mo. When the pressure is raised to 716 GPa, the frequencies along Γ-N in the TA branches soften...

We have developed a three level implicit method for solution of the Helmholtz equation. Using the cubic spline in space and finite difference in time directions. The approach has been modied to drive Numerov type nite difference method. The method yield the tri-diagonal linear system of algebraic equations which can be solved by using a tri-diagonal solver. Stability and error estimation of the...

aim and background: the purpose of this study was to compare patients with functional gastrointestinal disorders (fgid) and normal persons in terms of alexithymia, severity of gastrointestinal symptoms, and demographic variables. methods and materials: this causal-comparative research included 129 fgid patients who were referred to a psychosomatic disorders clinic in isfahan, iran. a matched gr...